Book: Probability and Statistics for Computer Scientists

Chapter 5

Exercise Problem 5.9

(Computer project) Twenty computers are connected to a network. One computer becomes infected with a virus. Every day, this virus spreads from any infected computer to any uninfected computer with probability 0.1. Also, every day, a computer technician takes 5 infected computers at random (or all infected computers, if their number is less than 5) and removes the virus from them. Estimate:

(a) the expected time it takes to remove the virus from the whole network; (b) the probability that each computer gets infected at least once;

(c) the expected number of computers that get infected.

How to approach this problem?